SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

3.4. TRANSPORT UNDER AN ELECTRIC FIELD 115

M ate rial B a ndga reak do wn el ec tr i c

(eV ) field (V/cm)

G aA s 1.43 4 x 10^5

G e 0.664 105

InP 1.34

S i 1.1 3 x 10^5

In0.53Ga0.47A s 0.8 2 x 10^5

C5.510^7

S iC 2.9 2-3 x 10^6

SiO 2 9–10^7

Si 3 N 4 5–10^7

GaN 3.4 2 x 10^6

pB

Table 3.2: Breakdown electric fields in some materials.

The tunneling probability through the triangular barrier is given by

T=exp

(

− 4

√

2 m∗Eg^3 /^2

3 eE

)

(3.4.14)

whereEis the electric field in the semiconductor.
In narrow bandgap materials this band-to-band tunneling or Zener tunneling can be very im-
portant. It is the basis of the Zener diode, where the current is essentially zero until the band-to-
band tunneling starts and the current increases very sharply. A tunneling probability of∼ 10 −^6
is necessary to start the breakdown process.

Example 3.9Calculate the band-to-band tunneling probability in GaAs and InAs at an

applied electric field of 2 × 105 V/cm.